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Take a random base 10 number of 32 digits. The odds of a run of 4 or more identical digits is about 1 in 40.

At First occurrence prime gaps by Dr. Thomas R. Nicely, you can see the minimal primes generating a given gap up to 1998. Things get weird after the 1800's. The odds of a run of 4 or more in these prime numbers is about 1 in 4. Is this some artifact of the sieving method?

23333096984797, 111113196467011, 67777708053772723, 404444692323376357, 316129781931380000239027, 6787988999657777797, 33631026000015061369578943, 302233338032699490171225683, 3281312000028041064344397077, 612233338029222068547009577, 5739248000028792850873302491, 5972248000023708695939463647, 7500230000000254312587886349, 612233338029577635338157403, 7500230000004410741095419811, 7051230000020674054592576303, 512233338030056680994432863, 7500230000005824418875087691, 2644230000031218882264673171, 5851230000021967795781669357, 612233338029038274818850137, 8511230000017373935165665319, 5844230000028765302725127593, 7500230000005019060037933673, 65013315500001000157495421077531, 3039248000030181434897238311, 2844230000030892453360363713, 8012239000018115133439311463, 3044230000030128405583745033, 17361011751029174933335986203, 6139248000028643882072689133, 15251000000439240915164391943, 8051230000019922137852468729, 7500230000011523034496281371, 85982514713000000005643994785767

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    $\begingroup$ I guess it could have something to do with "No gap exceeding 1510 has been definitively established as a first occurrence; larger gaps included in these lists are instead first known occurrence prime gaps." and ranges searched for primes. $\endgroup$ – Daniel Fischer Nov 3 '17 at 19:07
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    $\begingroup$ Most of these have strings of consecutive zeroes. In particular, there's a preponderance of 28-digit numbers of the form $xxxx230000\dots$ That seems like a human decision about where to start searching. $\endgroup$ – nickgard Nov 4 '17 at 19:14

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